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Square Root of 529

The square of 23 gives 529. Hence, 529 is a perfect square number. Thus, the square root of 529 is a rational number. In this mini-lesson we will learn to find square root of 529 along with solved examples. Let us see what the square root of 529 is.

Square Root of 529:√529 = 23
Square of 529: 529² = 2,79,841

1.	What Is the Square Root of 529?
2.	Is Square Root of 529 Rational or Irrational?
3.	How to Find the Square Root of 529?
4.	Important Notes
5.	Thinking Out of the Box!
6.	FAQs on Square Root of 529

What Is the Square Root of 529?

The square root of 529 is the integer which on squaring gives 529. Hence, the square root of 529 is 23. It is written as √529 = 23. Hence, 529 is a perfect square.

Is the Square Root of 529 Rational or Irrational?

As √529 = 23, it is possible to express √529 in p/q form easily. Hence, √529 a rational number.

How to Find the Square Root of 529?

There are numerous ways to determine the square root of any number. Click here to learn more about them.The square root of 529 can be found using two methods:

Square Root of 529 by Long Division
Square Root of 529 by Prime Factorization

Square Root of 529 by Long Division

The square root of 529 can be found using the long division using the below given steps:

Step 1: First we pair digits of a given number starting with a digit at one's place. Put a horizontal bar to indicate pairing.
Step 2: We find a number which on multiplication with itself gives a product less than or equal to 5. As we know 2 × 2 = 4 and 4 < 5. Hence, the difference is 1 and the quotient is 2.
Step 3: Now, we have multiply the quotient by 2. This give us 4. Hence, 4 is the starting digit of the new divisor.
Step 4: 3 is placed at one's place of new divisor because when 43 is multiplied by 3 we get 129. The obtained answer now is 0. Now the new divisor obtained is 46.
Step 5: Hence, the square root of 529 is 23.

Square Root of 529 by Long Division Method

Square Root of 529 by Prime Factorization

529 can also be expressed as (23 × 23). The number which get repeated within square root is 23. Hence, the square root of 529 is 23.

Thus, the square root of 529 is 23.

Explore square roots using illustrations and interactive examples

Important Notes:

529 is a perfect square number. Hence, the value obtained after taking its square root is a whole number.
The square root of 529 is simplified as 23 either by using the prime factorization of 529 or by expressing 529 as a square of 23.

Think Tank:

Is the value obtained by taking square root of 529 a decimal number?
Are -√529 and √-529 same?

Example 1: What is the difference in lengths of square boxes having area 529 square inches and 484 square inches?

Solution

As the area of square box is area = length × length
The length of square box having area 529 square inches is 529 = 23 inches.
Similarly, the length of box having area 484 square inches is √484 = 22 inches.
The difference in lengths of boxes is (23 - 22) inch = 1 inch.
Hence, the difference in length of square boxes having area 529 square inches and 484 square inches is 1 inch.
Example 2: Does the radius of circle having area 529π square inches have length of radius less than 20 inches?

Solution

Radius can be found using the formula of area of a circle is πr² square inches. By the given information,
πr² = 529π ⇒ r² = 529
By taking the square root on both sides we get, √r²= 529. We know that the square root of r² is r. By calculating the square root of 529 is 23 inches. Hence, the radius of circle having area 529π square inches will have length of radius more than 20 inches.

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FAQs on Square Root of 529

What are the two square roots of 529?

The two square roots of 529 are -23 and 23.

Is 529 a perfect square?

Yes, 529 is a perfect square.

Does 529 have a square root?

Yes, 529 has a square root. The √529 is 23.

Can square root of 529 simplified?

529 can be broken as a product of 23 × 23. The square root of 529 gives output as 23.

Is the square root of 529 rational or irrational?

The square root of 529 is rational.

Is square root of 529 a real number?

Yes, the square root of 529 is a real number.

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